Energy & Fuels 1987,1, 181-186 Table VI. Influence of Percent Observable Carbons in Macerals on Apparent NMR Aromaticity of a Hypothetical Coal Hypothetical Coal maceral exinite vitrinite inertinite
content
f.
f.of coal
10% 80 %
0.50 0.70
0.69
10%
0.80
NMR Analysis maceral exinite vitriite inertinite
% C obsd
100 35 25
content (NMR), % 25
f.(NMR)
69 6
0.65
In addition, the experimental bias in the NMR response seen among the maceral samples implies that the carbon aromaticities of whole coals would be underestimated even further. An example of this effect is shown in Table VI for a hypothetical coal having a normal maceral distribution and given representative fa values for its macerals. It is seen that the NMR analysis clearly over represents the exinite content in the sample, leading to a underestimation of the carbon aromaticity by about 6%. Of course, the magnitude of the effect depends on the maceral composition of the coal; in samples having a greater exinite and/or inertinite content, larger deviations from the theoretical value are possible. It is believed that these effects are responsible, a t least in part, for the scatter observed in the correlations of NMR fa values with other coal-rank parameters.
Summary Carbon-spin-counting experiments performed by using an internal intensity standard have demonstrated that a significant portion of the total organic carbon in three coals
181
is not detected. I t has been shown that the NMR signal in CP/MAS spectra is derived from 40-56% of the total carbon in these coals. The variation in signal response seen amongst macerals is found to be substantially greater, ranging from a truely quantitative response in the case of a hydrogen-rich resinite sample to only 26% of the carbon in fusinite. For the macerals, there is a systematic correlation between the unobserved carbon signal and both the free-electron spin density and H/C content of the sample under investigation. Problems arise in the analysis of samples with a low hydrogen content (H/C < l.O), whose free-radical content is in excess of about (3-5) X lOI9 spins/g, and these'problems can be traced to the direct dipolar interactions of the paramagnetic centers and/or to inefficient carbon polarization. The derived carbon aromaticities and relaxation parameters, together with quantification experiments, support a model for coal in which the macerals are phase separated and for which there is an experimental bias favoring the detection of the more hydrogen-rich macerals and a discrimination against the aromatic carbons. It is concluded that in unfavorable cases CP/MAS experiments underestimate the carbon aromaticity of coals by as much as 10-15%.
Acknowledgment. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U S . Department of Energy, under Contract No. W-31-109-ENG-38. The authors thank K. L. Stock for the maceral separations and P. C. Lindahl and I. M. Fox (Argonne Analytical Chemistry Laboratory) for elemental analysis. We also gratefully acknowledge Dr. R. B. Clarkson and the Illinois ESR Research Center a t the University of Illinois (NIH Grant No. RR01811) for the ESR measurements on macerals and Dr. Leo Lynch of CSIRO, Australia, for providing us with the Victorian brown coal sample.
Transport of Penetrants in the Macromolecular Structure of Coals. 6. Amine Transport Mechanisms Barbara D. Barr-Howell,?John M. Howell,' and Nikolaos A. Peppas* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907 Received July 28, 1986. Revised Manuscript Received October 20, 1986 Dynamic transport studies of n-propylamine, n-butylamine, diethylamine, and dipropylamine were performed on unextracted and pyridine-extracted coal samples. The results were analyzed by an exponential expression of the penetrant uptake as a function of time and by an in-series additive model including terms for the diffusional and relaxational mechanisms. It w p shown that the amine transport mechanism is highly non-Fickian, approaching case I1 transport, and that it depends on carbon content and sample size.
Introduction Investigation of the transport mechanisms of various solvents (penetrants) in glassy polymers has attracted significant research interest in recent years. The pioneering qualitative work of Brenner and his
* Author to whom correspondence should be addressed. Present address: Amoco Research Center, Naperville, IL 60540. 'Present address: L. J. Broutman & Assoc. Ltd., Chicago, IL 60616. 0887-0624/87/2501-0181$01.50/0
has revealed some of the unusual characteristics of penetrant transport in thin coal sections, including the detailed description of the penetrant from development in coal. (1)Brenner, D.Proc.-Znt. Kohleniuiss. Tag. 1981,I , 163-168. (2) Brenner, D.Prepr. Pap.-Am. Chem. Soc., Diu. Fuel. Chem. 1982, 27(3-4), 244-253. (3)Brenner, D.Nature (London) 1983,306,772-773. (4)Brenner, D.Fuel 1983,62, 1347-1350. (5) Brenner,D.;Hagan, P. S.Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel. Chem. 1985,30(1),71-82.
0 1987 American Chemical Society
182 Energy & Fuels, Vol. 1, No. 2, 1987
The work of Hsieh and Duda6J and some of the previous contributions of our group"" in this series have examined quantitative aspects of the vapor or liquid transport phenomenon. Our previous worke" has also discussed the crazing phenomenon associated with penetrant transport in coal. We have also offered, by analogy to well-known theoretical models applied to transport in glassy polymers, a preliminary analysis of the possible mechanism(s) of penetrant transport in coal networks. The reader should note that the goals of dynamic swelling of coal networks are significantly different from those of equilibrium swelling studies,12the latter providing an analysis of the solvent interactions with the coal network and preliminary evaluation of the cross-linked s t r ~ c t u r e . ' ~ - ' ~ Analysis of dynamic swelling results of macromolecular coal networks swollen by good solvents may also yield important information about solvent-network interactions and the structure of the network.8~~ Diffusion studies can be used to determine the thermodynamic state of the network, i.e. whether the network exists in the glassy or rubbery state. But the main purpose of these studies is to determine the mechanism of solvent uptake that occurs in the network. The solvent uptake can occur by Fickian diffusion, anomalous transport, case I1 transport, or super case I1 transport. The definition of these mechanisms and their relevance to penetrant transport of coals has been discussed before in our work."1° When a macromolecular network such as coal exists in the glassy thermodynamic state all large molecular chain motions are restricted, but the segmental motions are not necessarily limited. As the temperature of the network is increased to the glass transition temperature, large molecular chain motions become important and the network shifts to its rubbery thermodynamic state! The exact glass transition temperature of the macromolecular network is dependent on its chemical and physical nature. The presence of solvent can increase large molecular chain motions at lower temperatures, thereby effectively lowering the glass transition temperature of the network. The effect of temperature and penetrant activity on the transport mechanism in glassy structures has been discussed by Hopfenberg and Frisch.15 Anomalous diffusion occurs only below the glass transition temperature and a t fairly high penetrant activities. Fickian diffusion occurs both in the glassy state and the rubbery state. Concentration-independent Fickian diffusion occurs generally a t low penetrant activities or low temperatures. A convenient method of transport analysis employs fitting the sorption data to eq 1. Here Mt is defined as the mass of solvent uptake at time t , M , is the mass of solvent
(6) Hsieh, S. T.; Duda,J. L. Polym. Mater. Sci. Erg. 1984,51,703-706. (7)Hsieh, S.T.Ph.D. Thesis, Department of Chemical Engineering, The Pennsylvania State University, 1984. (8)Peppas, N. A.; Lucht, L. M. Chem. Eng. Commun. 1985, 37,
334-354. (9)Barr-Howell, B. D.; Peppas, N. A.; Winslow, D. N. Chem. Eng. Common. 1986,43, 301-315. (10)Barr-Howell, B. D.; Peppas, N. A.; Squires, T. G. J. Appl. Polym. Sci. 1986, 31, 39-53. (11)Ritger, P. L.; Peppas, N. A. Fuel, in press. (12)Green, T.; Kovac, J.; Brenner, D.; Larsen, J. W. In Coal Structure, Meyers, R. A., Ed.; Academic: New York, 1982;pp 199-282. (13)Lucht, L. M.;Peppas, N. A. Fuel, in press. (14)Larsen, J. W.; Green, T. K.; Kovac, J. J. Org. Chem. 1985, 50, 4729-4735. (15)Hopfenberg, H. B.; Frisch, H. L. J.Polym. Sci., Part B 1969, 7, 405-412. (16) Enscore, D. J.; Hopfenberg, H. B.; Stannett, V. T. Polymer 1977, 18,793-802.
Barr-Howell et al. Table I. Analysis of PSU Coal Samples anal., % (dmmf) PSOC mineral C 0 matter code no. county, state rank" 418 Titus, T X LigA 69.9 21.4 27.5 791 20.7 Titus, TX LigA 72.2 20.1 247 Burke, ND LigA 75.5 17.6 12.7 7.0 312 Navajo, AR HVC 78.3 14.1 853 Delta, CO HVC 80.1 12.6 3.7 402 Craig, OK HVA 82.4 9.0 18.5 989 Greenbrier, WV MVB 88.1 3.7 5.0 Key: LigA = lignite; HVC = high-volatile C bituminous; HVA = high-volatile A bituminous; MVB = medium volatile bituminous.
uptake as time approaches infinity, k is a constant dependent on the structural characteristics of the network, and n is the exponent that indicates the type of solvent uptake. Recently Ritger and Peppas" related the exponent n to the various types of diffusion for various geometrical shapes. Equation 1 is valid only in the analysis of the first 60% of the final mass of solvent uptake. For transport in spheres, n = 0.43indicates Fickian diffusion, whereas n = 0.85 indicates case I1 transport. For Fickian diffusion with constant boundary conditions'l and a constant diffusion coefficient, the sorption and desorption kinetics in spheres is given by eq 2. Here
Mt is the mass of solvent uptake at time t , M , is the mass of solvent uptake as time approaches infinity, r is the radius of the sphere, and D is the concentration-independent diffusion coefficient. For case I1 transport, which usually occurs a t high penetrant activity and is relaxation-controlled, the desorption and sorption data in a sphere are expressed16by eq 3. Here ko is defined as the case I1 relaxation constant (3) in g/(cm2 s) and is assumed to be a constant; co is the equilibrium concentration of the penetrant, and r is the radius of the sphere. Most diffusion data do not follow Fickian diffusion or case I1 transport kinetics but are explained by a combination of the two kinetic models. Anomalous transport may be described by coupling of the relaxation process with the diffusion process. This idea of coupling led Berens and H~pfenberg'~ to propose a model to describe this process as given in eq 4. Here @F and @R are the
I - - Mt =
M, @F[
5
1'
n2n = i n2
exp(-a2n2Dt/r2) + @R exp(-kt) (4)
fractions of sorption contributed by Fickian diffusion and the relaxation process respectively, D is the diffusion coefficient for the Fickian protion of the transport, and k is the first-order relaxation constant. If diffusion occurs rapidly in comparison to relaxation, both D and k can be determined from the sorption data. (17)Berens, A. R.;Hopfenberg, H. B. Polymer 1978, 19, 490-495.
Transport of Penetrants in Coals
Energy & Fuels, Vol. 1, No. 2, 1987 183 5.00, 4.50
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Figure 1. n-Propylamine uptake as a function of time at 35 "C and an activity of 1.0 for PSOC 418 with 69.9 %C (dmmf) ( O ) , PSOC 791 with 72.3 %C, (dmmf) (o),and PSOC 312 with 78.3 %C (dmmf) (A).
Figure 2. n-Propylamine uptake as a function of time at 35 O C and an activity of 1.0 for PSOC 853 with 80.1 %C (dmmf) ( O ) , PSOC 402 with 82.4 %C (dmmf) (01, and PSOC 989 with 88.1 %C (dmmf) (A).
The goal of this contribution is to examine the dynamic swelling of coals by analogous amines and to analyze the effects of various structural and other parameters on their transport mechanism.
Table 11. Equilibrium n -Propylamine Uptake per Mass of Untreated 600-850-fimCoal Particles at 35 "C penetrant uptake, PSOC code no. % C (dmmf) g/g of coal 418 69.9 3.96 i 0.15 72.7 3.69 f 0.19 791 247 75.5 3.20 i 0.02 312 78.3 3.34 f 0.20 853 80.1 3.25 i 0.07 402 82.4 1.89 i 0.06 989 88.1 0.16 f 0.01
Experimental Section Sample Preparation. The coal samples, average size of 600-850 pm and packed under nitrogen, were supplied by The Pennsylvania State University Coal Bank (PSU) (Table I). The samples were sieved under nitrogen to the desired mesh sizes and sealed and stored under nitrogen until use. The 20-30-mesh coal samples were prepared for study by exhaustive Soxhlet extraction with pyridine. The extraction process separated the sol portion from the gel portion of the coal samples. All extractions were carried out under nitrogen with pyridine used at ita atmospheric boiling point of 115.5 "C. The solvent was replaced every 1-4 days until the extract solvent appeared to run clear. The process required an extraction time of 4-20 weeks. Acetone was then used as the extraction solvent at 56.2 OC for 24 h under nitrogen to drive out the remaining pyridine. Approximately 10% pyridine remained irreversiblyadsorbed in the coal matrix. Transport Studies. Untreated coal samples of 1-2 g were dried and weighed to h0.005 g. They were then placed in 10-mL beakers, which were suspended in desiccators over a pool of solvent. The solvents used in the studies were n-propylamine, n-butylamine, diethylamine,and dipropylamine. The desiccators were sealed and suspended in a water bath to maintain a constant temperature of 35 "C. At set time intervals, the coal samples were removed, weighed, and then returned to the dessicators. Mercury Porosimetry Studies. Untreated 650-800-pm coal particles were dried under vacuum for approximately 24 h and then placed in a powder penetrometer. The sample and penetrometer were weighed and placed into the filling device where a vacuum was applied until approximately 50 pmHg of pressure was reached. Mercury was then introduced into the penetrometer. The vacuum was released in increments, and intrusion volumes were read directly from the penetrometer. At atmospheric pressure, the filled penetrometer was weighed and then placed into a high-pressure chamber. A piston pump was used to increase the pressure up to 41 m a . Intrusion volumes in the high-pressure regime were measured by using a change in capacitance. COIT~C~~OIIS for sample and mercury compressibilitywere madeg by carrying out the same procedure with 650-800-pm Ceylon graphite particles (Asbury Graphite Mills, Inc., Asbury, NJ). The intrusion volume calculated for the nonporous graphite was subtracted from the intrusion volumes for the coal samples. Corrections for interparticle volume were made by using untreated 650-800-gm particles of PSOC-384, a semianthracite with 94.1 %C (dmmf). Again the intrusion volume calculated from PSOC-384 was subtracted from the intrusion volumes of the coal
samples. More information on the exact method of porosimetry corrections can be found in the work of Barr-Howell et al.'
Results and Discussion Effect of Carbon Content on Dynamic Swelling, In the first set of experiments, the effect of carbon content on the sorption of n-propylamine vapor at a penetrant activity of 1.0 was studied. The samples were dried before experimentation and then exposed to n-propylamine vapor at 35 "C until equilibrium swelling had been established. The mass of solvent uptake per mass of coal sample (dmmf) was calculated as a function of time. The results of PSOC 418 with 69.9 %C (dmmf), PSOC 791 with 72.7 %C (dmmf), and PSOC 312 with 78.3 %C (dmmf) are shown in Figure 1. The results for PSOC 853 with 80.1 %C (dmmf), PSOC 402 with 82.4 %C (dmmf), and PSOC 989 with 88.1 %C (dmmf) are shown in Figure 2. Experimental error for these studies was on the order of 0.06%. The first major observation from this set of experiments was the dramatic effect of carbon content on the final solvent uptake per mass of coal sample (dmmf) as shown in Table 11. The solvent uptake decreased with increasing carbon content. This supports the idea that the higher ranked coals are more ordered and crosslinked in comparison to the lower ranked coals. The dynamic swelling studies showed that penetrant uptake increased as a function of time, rather quickly for approximately the first 60 h and then slower, until equilibrium was established above 100 h. The graphs of npropylamine uptake as a function of time show two inflection points, which may be indicative of mechanistic deviations from Fickian diffusion or simply of experimental uncertainty. The latter situation should be probably excluded due to the small error (0.06%) of the technique.
Barr-Howell et al.
184 Energy & Fuels, Vol. 1, No. 2, 1987 Table 111. Analysis of the Sorption Data from the n -Propylamine Swelling Studies of 600-850-~mParticles at 35 "C and an Activity of 1.0 Using Ea 1" 95 % PSOC confidence code no. %C (dmmf) k exponent n limits 0.74 f0.03 418 69.9 0.07 0.83 10.03 791 72.7 0.05 247 75.5 0.02 0.98 f0.03 zk0.03 0.05 0.79 312 78.3 0.79 f0.02 853 80.1 0.04 f0.03 0.05 0.68 402 82.4
q'Oo 3.60
3
nPenetrant uptake in coal PSOC 989 (88.1 %C, dmmf) was too small for valid analysis.
Table IV. Diffusion Coefficients and Relaxation Constants" from the n -Propylamine Studies at 35 "C and at an Activity of 1.0 Calculated by Using Eq 4 %C PSOC code no. (dmmf) k, s-l D, cm2/s 418 69.9 11.0 x 10+ f 7.46 X lo4 f 3.3 x 10-9 2.2 x 10-12 2.80 X lo4 f 791 72.2 5.53 x 10" f 2.8 x 10-9 2.80 x 10-9 2.24 X lo4 f 247 75.5 6.19 X lo4 1.5 X lo-* 5.4 x 10-12 312 78.3 7.9 x 104 f 3.2 x 10-9 f 2.4 x 10-9 9.4 x 10-3 853 80.1 5.80 X 10" f 2.24 x 10-9 1 5.8 X 6.4 x 10-13 402 82.4 4.23 X lo+ f 5.60 x 10-9 i 2.1 x 10-12 1.6 x 10-9 a
Including standard deviation.
Two methods were used to analyze the sorption data. The results from the fitting of the data of the first 60% of the final solvent mass uptake by using eq 1 are given in Table 111. The results show no direct correlation between the carbon content and the values determined for exponent n; however, all the values fall between 0.43 and 0.85, and therefore all the sorption mechanisms may be classified as anomalous transport approaching case I1 transport. The model of Berens and H ~ p f e n b e r g 'given ~ by eq 4 was used to determine n-propylamine diffusion coefficients and coal network relaxation constants. Table IV gives the results from this analysis. Here both the relaxation constants and the diffusion coefficients are found to decrease with increasing carbon content. Effect of Particle Size. A second set of dynamic swelling desiccator studies was designed to determine the effect of particle size on the mechanism of solvent transport. Again the samples were predried and then exposed to n-propylamine vapor (activity of 1.0) a t 35 O C until equilibrium swelling had been established. The results from these swelling experiments were plotted as the mass of n-propylamine uptake per mass of coal sample (dmmf) as a function of time; these results are given in Figure 3, for PSOC 312 with 78.3 %C (dmmf) with sizes of 850-600, 600-425, 425-250, 250-180, and 180-150 wm. Again the curves of penetrant uptake vs. time show deviations from typical Fickian diffumn curves. Since all the samples studied in these experiments have the same structure, it is important to note that they should all come to basically the same equilibrium value. The fact that one sample had a higher equilibrium value is the result of inhomogeneities between the samples and slight variations in the experimental procedure. To determine the mechanism of penetrant transport, the data were analyzed by using eq 1 as shown in Table V. A decrease in particle size was found to cause a decrease in
0.00
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90
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TIME I H R ) Figure 3. Penetrant uptake as a function of time for the npropylamine studies on PSOC 312 with 78.3 %C (dmmf) with particle sizes of 850-600 (0),600-425 (a),425-250 (A),250-180 (O), and 180-150 pm (v)at a temperature of 35 "C and an activity of 1.0.
Table V. Analysis of the Sorption Data for PSOC 312 with 78.3 %C (dmmf) of Varying Sizes with n-Propylamine as the Solvent at 35 "C and an Activity of 1.0 Using Ea 1 95% particle exponent confidence size, fim k n limits 850-600 0.05 0.79 10.03 600-425 0.07 0.72 f0.02 425-250 0.10 0.67 10.02 250-180 0.12 0.62 f0.02 180-150 0.13 0.54 f0.02 Table VI. Effect of Particle Size on the Relaxation Constants and Diffusion Coefficients" for PSOC 312 with 78.3 %C (dmmf) with n -Propylamine as the Solvent at 35 "C and an Activity of 1.0 Using Eq 4 particle size, pm k , s-l D, cm2/s " I 79.0 x 10-5 f 2.4 x 10-9 3.2 x 10-9 f 9.4 x 10-13 600-425 1.04 X f 3.4 X loFs 1.4 X f 4.6 X 425-250 1.31 X f 1.8 X lo-' 4.84 X f 6.8 X 250-180 1.61 X f 1.4 X lo-' 1.16 X lo-' f 1.0 X 180-150 1.56 X f 5.7 X 0.447 X 11.6 X lo-" Including standard deviation.
the value of the exponent n. This indicates a shift from anomalous transport in the larger particles to almost Fickian diffusion in the smaller particles. The same type of shift in the mechanism of solvent transport has also been observed in the study of polymer networks. The mathematical analysis of the dynamic swelling studies to determine the effect of particle size on diffusion coefficients and relaxation constants was carried out by using the model of Berens and Hopfenberg,17 which is given by eq 4. The diffusion coefficients (Table VI) were not expected to change as the particle size decreased; however, an attempt to force the diffusion coefficients to remain constant resulted in the fraction of sorption contributed by Fickian diffusion to be greater than one. Since this is physically impossible, the diffusion coefficients were allowed to vary. These results indicate a possible weakness in the model of Berens and H0~fenberg.l~ Alternatively, the small variation of the diffusion coefficient around an average value of 2.2 x cm2/s may be explained as an indication of an adequately constant value of the diffusivity (see data of Table VI). The relaxation constants are found to decrease with decreasing particle size, which is con-
Transport of Penetrants in Coals 5.00
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TIME [HRI Figure 4. Penetrant uptake as a function of time for the n-butylamine studies on PSOC 418 with 69.9 %C (dmmf),( O ) ,PSOC 312 with 78.3 %C (dmmf) (a), and PSOC 402 with 82.4 %C (dmmf) (A)at 35 "C and an activity of 1.0. Table VII. Equilibrium n -Butylamine Uptake per Mass of Coal Sample (dmmf) for 600-850-pm Particles at 35 O C as a Function of Carbon Content PSOC %C equilibrium uptake, code no. (dmmf) g/g of coal 418 69.9 4.77 f 0.31 312 78.3 3.69 0.19 402 82.4 2.25 f 0.07
*
sistent with a loss of non-Fickian behavior as particle size is reduced. Other Aliphatic Amines as Penetrants. A study of transport of other aliphatic amines for 600-850-wm coal particles was the final set of dynamic desiccator swelling studies. PSOC 418 with 69.9 %C (dmmf), PSOC 312 with 78.3 %C (dmmf), and PSOC 402 with 82.4 %C (dmmf) were exposed to n-butylamine vapor (activity of 1.0) at 35 "C until equilibrium swelling had been established. The resuIts from these studies are given in Figure 4 with the mass equilibrium values presented in Table VII. Comparison of these swelling studies with those of Figures 1 and 2 show that initially the swelling with n-butylamine is lower than the swelling with n-propylamine. Since nbutylamine is the larger molecule, these results show that the penetrant size affects transport. However, as the time of swelling exceeded 70 h the uptake of n-butylamine surpassed the uptake of n-propylamine (compare Tables I1 and VII). This increase may be the result of changes in the pore structure during the swelling process. Initially the n-butylamine entered the coal structure slower than the n-propylamine; however, as time increased the n-butylamine could have opened up the pore structure, which would have allowed the solvent to enter faster. Electrondonor and electron-acceptor interactions'* may also have contributed to these swelling properties; however, the information on these interactions for these aliphatic amines is not available, and therefore no conclusions may be drawn. Larsen and Leelg and Green and Westz0have studied the volume equilibrium swelling of Bruceton and Illinois No. 6 coals, among others, in various amines at low temperatures. The two common solvents, of their studies and ours (n-propylamine and n-butylamine), gave similar (18)Marzec, A.;Juziva, M.; Betley, K.; Sobkowiak, M. Fuel Process. Technol. 1979,2,35-44. (19)Larsen, J. W.; Lee, D. Fuel 1985,65,981-984. (20)Green, T.K.;West, T. A. Fuel 1986,65,298-299.
Table VIII. Analysis of the n -Butylamine Sorption Data from Dynamic Swelling Studies at 35 "C and an Activity of 1.0 on 600-850-pm Coal Particles Using Eq 1 95% PSOC %C exponent confidence code no. (dmmf) k n limits 418 69.9 0.031 0.75 h0.03 312 78.3 0.033 0.74 *0.03 402 82.4 0.042 0.68 f0.04
Table IX. Diffusion Coefficients and Relaxation Constants" from the n-Butylamine Studies at 35 "C and an Activity of 1.0 on 600-850-rm Coal Particles Calculated by Using Eq 4 PSOC %C code no. (dmmf) k , s-l D, cm2/s 418 69.9 4.5 X lo4 f 3.6 1.9 X 5.0 X x 10-10 312 78.3 4.5 X 10" f 1.2 1.9 X 1.9 X lo-'' x 10-10 402 82.4 2.9 X 10" f 2.9 0.96 X 10" 9.6 X x 10-10
* * *
Including standard deviation. 5.00
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Figure 5. Penetrant uptake as a function of time for PSOC 312 with 78.3 %C (dmmf) swollen with n-propylamine (o), n-butylamine (A),diethylamine (O), and dipropylamine (0) at 35 "C and an activity of 1.0. swelling behavior. These investigators offered further explanations for the preferential amine sorption in and swelling by certain coal structures. The mechanism of n-butylamine transport was determined by using eq 1, and the results are given in Table VIII. These results indicate that the mechanisms of solvent transport are the same for n-butylamine and npropylamine. This further corroborates the idea that as time increases the n-butylamine may open up the pore structure while at short times the transport mechansisms are the same. The diffusion coefficients and relaxation constants were determined from the model of Berens and Hopfenberg17 given by eq 4 and are found in Table IX. The results follow the same trends as those for the n-propylamine studies. The relaxation constants and the diffusion coefficients both decrease with increasing carbon content. The relaxation constants for both studies are nearly the same, indicating the same types of relaxations were occurring during both swelling processes. However, the diffusion coefficients for the n-butylamine studies are 1 order of magnitude larger than those for n-propylamine. This may again be the result of the opening up of the pore structure by the n-butylamine.
Barr-Howell et al.
186 Energy & Fuels, Vol. 1, No. 2, 1987 Table X. Equilibrium Penetrant Uptake per Mass of Coal (dmmf) for 600-850-pm Particles of PSOC 312 with 78.3 %C (dmmf) at 35 O C equilibrium equilibrium uptake, uptake, penetrant g / g of coal penetrant g/g of coal n-propylamine 3.34 f 0.20 diethylamine 1.92 f 0.04 n-butylamine 3.69 f 0.19 dipropylamine 0.08 f 0.00 Table XI. Analysis of the Sorption Data for Penetrant Uptake at 35 "C and an Activity of 1.0 for 600-850-pm Particles of PSOC 312 with 78.3 %C (dmmf) Using Eq 1 95 % confidence penetrantn k exponent n limits 0.05 0.79 f0.04 n-propylamine n-butylamine 0.03 0.74 f0.03 0.02 0.83 f0.02 diethylamine Dipropylamine uptake was too small for valid analysis.
Finally, diethylamine and dipropylamine vapor swelling studies were performed to study the effect of chain size of penetrant on the transport process. Figure-5 gives the results from penetrant uptake of n-propylamine, n-butylamine, diethylamine, and dipropylamine by 600-850-pm particles of PSOC 312 with 78.3 %C (dmmf). Table X shows the equilibrium swelling values. The uptake of diethylamine was slightly more than half the uptake of either n-propylamine or n-butylamine; however, the uptake of dipropylamine was minimal. This indicates that diethylamine and dipropylamine are poorer solvents for the coal network. The mechanisms of diffusion were determined for these four solvents by using eq 1,and the results are tabulated in Table XI. The penetrant uptake of dipropylamine was too small for any valid analysis. The other three solvents all demonstrated case I1 transport.
Discussion The studies of coal networks swollen with n-propylamine revealed the effect of particle size on the transport properties of the networks. It was found that as the particle size was reduced, the penetrant uptake approached Fickian diffusion. The Deborah number, which characterizes the nature of the transport mechanism and the coupling of diffusional and relaxational mechanisms is defined by eq 5. Here X
X
De = 8
(5)
is the characteristic relaxation time of the macromolecular network and 8 is the characteristic diffusion time of the penetrant in the network structure. The characteristic diffusion time can be approximated with eq 6. Here 1 is
Orz 12
(6)
the characteristic dimension of the sample, for these studies the average radius of the particles, and D is the
Table XII. Results from the Analysis of the Deborah Number To Determine the Effect of Particle Size for PSOC 312 Swollen by n -Propylamine Vapor at 35 "C Darticle size, um De Darticle size. um De -1 250-180 6.9 850-600 0.88 180-150 7.0 600-425 425-250 6.9 ~
~~~
penetrant diffusion coefficient. Substitution of this relationship into eq 5 leads to eq 7. For penetrant uptake that De
AD =-
(7)
12
is characterized as case I1 transport, De is approximately 1, and it becomes possible to obtain an estimate of the characteristic relaxation time, A, for the network. The Deborah numbers for the various particle sizes of PSOC 312 swollen with n-propylamine vapor at 35 "C are given in Table XII. The characteristic relaxation time, A, was calculated by using the data from the 600-800-pm particles of PSOC 312 and was found to be 4.1 X lo5 s for all the PSOC 312 samples swollen with n-propylamine. Deborah numbers on the order of 1 are indicative of case I1 transport in a glassy network with coupled relaxational and diffusional processes. The larger particles exhibited this type of diffusion. As the Deborah number becomes larger the diffusion process approaches Fickian diffusion through a glassy polymer. The smaller particles exhibited behavior of this type. This analysis corroborates the results found in Table V where as the particle size was decreased, the diffusion process approached Fickian diffusion. This type of analysis is frequently used to estimate the characteristic relaxation times and the Deborah numbers for polymeric systems, and therefore it is applicable in the study of cross-linked macromolecular systems.
Conclusions Amine transport in coal microparticles was investigated. In general, studies involving n-propylamine as the penetrant at 35 "C demonstrated the effect of particle size on the penetrant uptake. A shift from larger particles to smaller particles resulted in a shift from anomalous transport to almost Fickian diffusion. Analysis of the relaxation constants confirmed these results. Studies using analogous aliphatic amines indicated the solvent size does affect the penetrant uptake. The larger molecules diffuse more slowly. However, the need to determine the electron-donor and electron-acceptor numbers to explain the diffusion is noted. Acknowledgment. This work was supported by Department of Energy Grant No. DE-PG22-83PC 60792. We wish to thank Dr. Douglas Brenner and Professors Larry Duda and John Larsen for helpful discussions and insightful comments. This work was presented in preliminary form at the 189th National Meeting of the American Chemical Society, Miami Beach, FL, April 1985. Registry No. H3C(CH2)2NHz,107-10-8; H3C(CHz)3NHz, 109-73-9; (H3CCHZ)zNH, 109-89-7; (H,C(CH*)z)zNH, 142-84-7.
